Question

Given `f(x)=3x^4-2x^2` & `g(x)= 2/sqrtx, (x ≠0)` how do you find the composition of f and g?

Answer 1

See explanation.

Explanation:

There are two ways of composing 2 functions:

• `f(g(x))`

To find this composition you have towrite the formula of `g(x)` for every `x` in the formula of `f`. Here we get:

`f(g(x))=3*g^4(x)-2*g^2(x)`

`f(g(x))=3*(2/sqrt(x))^4-2*(2/sqrt(x))^2`

`f(g(x))=3*16/x^2-2*4/x=48/x^2-8/x=(8*(6-x))/(x^2)`

• `g(f(x))`

To find this composition you have towrite the formula of `f(x)` everywhere `x` is in the formula of `g`. Here we get:

`g(f(x))=2/(sqrt(f(x)))=2/sqrt(3x^4+2x^2)`